Transverse spin in the light-ray OPE

Abstract

Abstract We study a product of null-integrated local operators O 1 $$ {\mathcal{O}}_1 $$ and O 2 $$ {\mathcal{O}}_2 $$ on the same null plane in a CFT. Such null-integrated operators transform like primaries in a fictitious d − 2 dimensional CFT in the directions transverse to the null integrals. We give a complete description of the OPE in these transverse directions. The terms with low transverse spin are light-ray operators with spin J 1 + J 2 − 1. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins J 1 + J 2 − 1 + n, constructed using special conformally-invariant differential operators that appear precisely in the kinematics of the light-ray OPE. As an example, the OPE between average null energy operators contains light-ray operators with spin 3 (as described by Hofman and Maldacena), but also novel terms with spin 5, 7, 9, etc. These new terms are important for describing energy two-point correlators in non-rotationally-symmetric states, and for computing multi-point energy correlators. We check our formulas in a non-rotationally-symmetric energy correlator in N $$ \mathcal{N} $$ = 4 SYM, finding perfect agreement.

Keywords

• Field Theories in Higher Dimensions
• Nonperturbative Effects
• Scale and Conformal Symmetries